4 (a) Evaluate lim,1 (금-) (b) Let f(z) = -r. Find the value(s) of z if the second derivative f"(x) equals zero. (c) For what value(s) of r does the graph f(x)-구-교+3

Q: Evaluate the limit of the function: lim f(x) =- /7 +x -V7

A: topic - limits

Q: 1. (a) Using the limit definition of the derivative only, find f'(x) where f(x) = x. If you use any…

A:

Q: Use the definition of the derviative to compute the derivative of f(x) = at the specific х 3.…

A: We will obtain the answer in two steps: We will simplify the difference quotient We will then…

Q: Estimate the one-sided limits for the function below.  f(x)=(11−x)/(x−8)^2   lim f(x)= x-->8+…

A: Given function is

Q: Determine whether the shown statement makes sense or does not make sense, and explain your…

A: The functions whose graphs can be drawn without lifting the pencil off the paper is a continuous…

Q: Hence, find the value of lim f(x). x→-3 lim f(x) Enter your next step h x→-3

A: Given,          Consider the graph of a function, fx , shown below :

Q: B. Find the limit. Зх — 1 5. lim х-1/3 9х2-1 x3 - 1 6. lim х+1 х-1

A: As per our guidelines we are supposed to answer only 3 subparts

Q: 3 If lim f(x) = 3.5 and lim,-2+ f(x) = 6.5 the function has a double sided %3D x-2- limit or one…

A: A limit is the value that a function approaches as the input of that function approaches a certain…

Q: Sketch the graph of any function that satisfies the given conditions. x-intercept at -1 and…

A:

Q: (a) Find the equation of the tangent line to the curve 4x y-3x2 +5y = 10, at the point (1,-1).…

A: a)

Q: State the definition of the derivative of a function f. Use the definition of the derivative to…

A:

Q: tan 3h 3. Estimate the value of lim by creating a table of function values for h h = 0.01, 0.001,…

A: Let y=tan(3h)h Then we make tables for the given values. h y 0.01 3.00090032412 0.001…

Q: lim 극 et – 1 x-1

A:

Q: Once you know lim x-->a+ f(x)  and lim x-->a-  ƒ(x) at an interior point of the domain of ƒ,…

A: If we know the right and left-hand limit of a point then we know the limit at that point.

Q: Let ƒ(x) = (x2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01,…

A: Simplify f(x) first for x not equal to -3 x y -3.1 -6.1 -3.01 -6.01 -3.001 -6.001…

Q: b. f(3) = 2 and lim f (x) does not exist.

A:

Q: Suppose that a function f(x) is defined for all real values of x except at r = c. Does it imply the…

A: Here we have to check whether the limit exists or not.

Q: Sketch a possible graph of a function that satisfies the conditions below. (0) 0, lim f(x) - 1; lim…

A:

Q: Let g(x) = xe-* + be-*, where b is a positive constant. Find lim g(x).

A:

Q: Use the definition of the derivative to compute the derivative of the function f(x) : using algebra…

A:

Q: State the definition of the derivative of a function f. Use the definition of the derivative to…

A:

Q: Sketch the graph of the function and use it to determine the values of a for which limx--a f (x)…

A: We will find out the required values.

Q: Why is it important to know the concept of limits and limit of a function? Explain thoroughly

A: Concept of limit is very useful as this gives us the intense idea of approaching towards infinity.…

Q: Find a formula for a function f that satisfies the following conditions. lim fx) = 0, lim f(x) - -0,…

A: Function

Q: Sketch the graph of a function f (x) that satisfies the following conditions: limx -→ -o f (x) = o ;…

A: Follow the steps to sketch the graph.

Q: 6. State the definition of the derivative of a function f. Use the definition of the derivative to…

A:

Q: Sketch the graph of an example of a function fthat satisfies all of the given conditions. lim fx)2,…

A: Following information has been provided in the question,

Q: Use the definition of the derivative f'C)=lim flxty-PG4. to compuke derivative of flx)= 3X-X

A:

Q: Evaluate lim-[(sinx-x)/x³] by u

A:

Q: 3) lim (x² + 1) X--1

A: Limit is a basic concept of calculus  which shows the behaviour of a function  when it tends to that…

Q: If lim f(x) =5 x-->1- and lim f(x)=5 x-->1+, what can you say about lim f(x) x-->1? What can you say…

A:

Q: 28. Use the limit definition, lim 7 (x+h)- f(x) to determine the derivative of x-1. [Value of 4] h0

A:

Q: evaluate lim f (x) and lim f(x). X--00 -5 + 2e-* f(x) = %3D 5e-+6

A: f(x)=-5+2e-x5e-x+6limx→∞f(x)=limx→∞-5+2e-x5e-x+6             =limx→∞-5+2ex5ex+6…

Q: If f and g are two functions such that lim f(x) as x --> a = + infinity and lim g(x) as x --> a = +…

A: Given: f & g are two functions such that, To check if this statement is True or False

Q: 3 - – If lim f(x) = 3.5 and lim,-2+ f(x) = 6. 5 , the function has a double sided %3D x→2- limit or…

A: Given,          limx→2-fx=3.5 and limx→2+fx=6.5We know that,           Condition of double sided…

Q: 1. Evaluate lim f(x) if f(x) = {, if xs-1 &² - 2 if x>-1

A: Given function fx=1x,   if x≤-1x2-2 ,     if x>-1 We have to find  limx→0 fx=?

Q: The function f(x) of the below graph is discontinuous at x = -1 because: a) f(-1) does not exist b)…

A:

Q: Find lim f(x) given the graph of

A: Given that: Graph of the function:

Q: 3- If lim f(x) = 3.5 and lim,2+ f(x) = 6.5 , the function has a double sided x-2- limit or one sided…

A:

Q: Suppose y = f(x) is defined for all x. Sketch a graph with the indicated property. discontinuous at…

A: See the attachment

Q: 2) Use the definition of the derivative f(x+h)-f(x) lim hー→0 to find the derivative of f(x) =…

A: Our objective is to find the derivative using definition.

Q: 1) If lim f(x) = , what asymptotic behavior will be illustrated in the graph of f (x)?

A: 1) If limx→6-fx=∞, then the value of the function fx tends to infinity as x→6 from the left hand…

Q: State whether lim f (x) and f(c) are equal or unequal at the given value of c. Also, state whether…

A: Limiting value of the function is value that function seem to approach as it reaches certain value.…

Q: Consider the function…

A: The graph of f is as follows:

Q: Use the definition of the derivative to compute the derivative of the function f(x) = 1 – 6x at an…

A: We plug the given expression of f(x) in the limit. This is the difference quotient.

Q: 3 - If lim f(x) = 3.5 and lim,-2+ f(x) = 6.5 the function has a double sided %3D limit or one sided…

A:

Q: Show that a function cannot have two different limits at the same point. That is, if limx-->c…

A: Let f(x) be a function which is defined everywhere in an interval except x=a, then , If for all ,…

Q: What type of discontinuity is at x = 3, if lim f (x)= 0 and lim f (x)= 0? x-3 x>3* What type of…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.